Perverse sheaves on infinite-dimensional stacks, and affine Springer theory

The goal of this work is to construct a perverse t-structure on the ∞-category ℓ-adic LG-equivariant sheaves loop Lie algebra Lg and show that affine Grothendieck–Springer sheaf S perverse. Moreover, an intermediate extension its restriction locus “compact” elements with regular semi-simple reduction. Note classical methods do not apply in our situation because LG are infinite-dimensional ind-schemes.